Model Diagnostics in the presence of measurement error

The problem of using information available from one variable X to make inferenceabout another Y is classical in many physical and social sciences. In statistics this isoften done via regression analysis where mean response is used to model the data. Onestipulates the model Y = µ(X) +ɛ. Here µ(X) is the mean response at the predictor variable value X = x, and ɛ = Y - µ(X) is the error. In classical regression analysis, both (X; Y ) are observable and one then proceeds to make inference about the mean response function µ(X). In practice there are numerous examples where X is not available, but a variable Z is observed which provides an estimate of X. As an example, consider the herbicidestudy of Rudemo, et al. [3] in which a nominal measured amount Z of herbicide was applied to a plant but the actual amount absorbed by the plant X is unobservable. As another example, from Wang [5], an epidemiologist studies the severity of a lung disease, Y , among the residents in a city in relation to the amount of certain air pollutants. The amount of the air pollutants Z can be measured at certain observation stations in the city, but the actual exposure of the residents to the pollutants, X, is unobservable and may vary randomly from the Z-values. In both cases X = Z+error: This is the so called Berkson measurement error model.In more classical measurement error model one observes an unbiased estimator W of X and stipulates the relation W = X + error: An example of this model occurs when assessing effect of nutrition X on a disease. Measuring nutrition intake precisely within 24 hours is almost impossible. There are many similar examples in agricultural or medical studies, see e.g., Carroll, Ruppert and Stefanski [1] and Fuller [2], , among others. In this talk we shall address the question of fitting a parametric model to the re-gression function µ(X) in the Berkson measurement error model: Y = µ(X) + ɛ; X = Z + η; where η and ɛ are random errors with E(ɛ) = 0, X and η are d-dimensional, and Z is the observable d-dimensional r.v.

Regional climate model applications on sub-regional scales over the Indian monsoon region: The role of domain size on downscaling uncertainty

Regional climate models are becoming increasingly popular to provide high resolution climate change information for impacts assessments to inform adaptation options. Many countries and provinces requiring these assessments are as small as 200,000 km2 in size, significantly smaller than an ideal domain needed for successful applications of one-way nested regional climate models. Therefore assessments on sub-regional scales (e.g., river basins) are generally carried out using climate change simulations performed for relatively larger regions. Here we show that the seasonal mean hydrological cycle and the day-to-day precipitation variations of a sub-region within the model domain are sensitive to the domain size, even though the large scale circulation features over the region are largely insensitive. On seasonal timescales, the relatively smaller domains intensify the hydrological cycle by increasing the net transport of moisture into the study region and thereby enhancing the precipitation and local recycling of moisture. On daily timescales, the simulations run over smaller domains produce higher number of moderate precipitation days in the sub-region relative to the corresponding larger domain simulations. An assessment of daily variations of water vapor and the vertical velocity within the sub-region indicates that the smaller domains may favor more frequent moderate uplifting and subsequent precipitation in the region. The results remained largely insensitive to the horizontal resolution of the model, indicating the robustness of the domain size influence on the regional model solutions. These domain size dependent precipitation characteristics have the potential to add one more level of uncertainty to the downscaled projections.

A New Model For Reliability Centered Maintenance In Petroleum Refineries

Refiners today operate their equipment for prolonged periods without shutdown. This is primarily due to the increased pressures of the market resulting in extended shutdown-to-shutdown intervals. This places extreme demands on the reliability of the plant equipment. The traditional methods of reliability assurance, like Preventive Maintenance, Predictive Maintenance and Condition Based Maintenance become inadequate in the face of such demands. The alternate approaches to reliability improvement, being adopted the world over are implementation of RCFA programs and Reliability Centered Maintenance. However refiners and process plants find it difficult to adopt this standardized methodology of RCM mainly due to the complexity and the large amount of analysis that needs to be done, resulting in a long drawn out implementation, requiring the services of a number of skilled people. These results in either an implementation restricted to only few equipment or alternately, one that is non-standard. The paper presents the current models in use, the core requirements of a standard RCM model, the alternatives to classical RCM, limitations in the existing model, classical RCM and available alternatives to RCM and will then go on to present an ‗Accelerated‘ approach to RCM implementation, that, while ensuring close conformance to the standard, does not place a large burden on the implementers